8/22/2019 dfrgrgccccccccccccccccccccccccccccccccccccccccccccccccccccccccccccccccccccccccccccccccccccccccccccccccccccccccccccc

http:///reader/full/dfrgrgccccccccccccccccccccccccccccccccccccccccccccccccccccccccccccccccccccccccccccccccccccccccccc 1/2

Power-Aware Routing and Wavelength Assignment in Optical Networks

Yong Wu, Luca Chiaraviglio, Marco Mellia, Fabio Neri

Politecnico di Torino, Corso Duca Degli Abruzzi 24, 10129, Torino, Italy B luca.chiaraviglio@polito.it

Abstract We introduce the Power-Aware RWA problem, whose goal is to accommodate lightpaths in wavelength

routing networks minimizing the power consumption. Formulation, algorithms, and results are presented, showing

that significant power savings are possible.

Introduction

Wavelength Routing (WR) networks offer the flexibility

of designing a logical topology, comprising lightpath

requests, over a physical topology, comprising OXCs

and links with many fibers each. The Routing and

Wavelength Assignment (RWA) problem is well known

in the literature [1]. Its goal is to assign a route and

a suitable wavelength in the physical topology for eachlightpath of the logical topology. Traditionally, the goal

of the RWA problem is to minimize the load (e.g., num-

ber of wavelengths) on available resources, in order

to maximize the probability of accommodating possible

new lightpath requests. However, this leads in general

to a waste in the power required to keep up and run-

ning both OXCs and optical amplifiers along fiber links.

Given the large number of these devices (thousands)

and their power footprint (up to tens of kW), we propose

to target the minimization of power consumption when

solving the RWA problem, by making maximum usage

of powered-on devices, e.g., by reusing the same fiber

along the same path as much as possible, in contrast to

spreading lightpaths on available fibers and paths. We

name this problem Power-Aware RWA (PA-RWA) prob-

lem. In this paper, we give a formulation of the problem,

propose heuristics to solve it, and present simulation

results showing that a large amount of power can be

saved in WR networks, reducing up to a factor of 5 the

energy (and the cost) needed to operate a WR network.

Problem Formulation

The PA-RWA problem can be defined using an integer

linear programming (ILP) formulation. Let sd denote

the number of lightpath requests from source s to des-tination d, and sdw the number of lightpaths from s to

d on wavelength w: sd =

wsdw. Let f

sdwijk {0, 1}

denote the number of lightpaths from s to d on fiber k

of link (i, j) using wavelength w, and fsdwij =

kfsdwijk .

On link (i, j), let Kij be the number of fibers, and Fijkthe number of wavelengths available on fiber k. Let aijk

be the number of amplifiers on fiber k of link (i, j), and

xijk {0, 1} be binary variables equal to 1 if fiber k

on link (i, j) is used to route a lightpath. Similarly, let

yi {0, 1} be binary variables equal to 1 if OXC i is

used. Finally, let PA and PO be the power consump-

tions of one amplifier and one OXC, respectively. We

do not consider the possibility of powering off individ-

This work was partially supported by the BONE research project.

ual transceivers or subsystems in OXCs. The notation

above leads to the following ILP formulation of the PA-

RWA problem:

min Ptot; Ptot = PAi,j,k

aijkxijk + POi

yi (1)

s.t.s,d

fsdwijk 1 w,i,j ,k (2)

s,d,w

fsdwijk M xijk i,j ,k (3)

j,k

xijk +j,k

xjik Myi i (4)

k

fsdwijk = f

sdwij s ,d,w,i,j (5)

i

fsdwij f

sdwji

=

sdw, j = s

sdw, j = d s ,d,w,j

0, j = s, d

(6)

s,d,w

fsdwijk Fijk i,j ,k;

k

xijk Kij i, j (7)

Eq. 1 is the utility function. Eq. 2 constraints a wave-

length on a fiber to be assigned to at most one light-

path; Eq. 3 imposes that a fiber is used if at least one

wavelength is assigned (M, and later M, are sufficient

large constants); Eq. 4 state that OXC i has to be pow-

ered on if any of its fibers is used; Eq. 5 counts the

number of fibers; Eq. 6 are the classical routing con-

straints, assuming no wavelength conversion function-

ality; finally Eqs. 7 limit the number of wavelengths on

each fiber, and the number of fibers in each link.

Algorithms

Following a well-established approach, the problem is

divided in two parts: routing and fiber&wavelength as-

signment. Considering the routing problem, we imple-

mented three heuristics: Least-Cost Path (LCP) [1],

Most-Used Path (MUP) and Ordered-Lightpath Most-

Used Path (OLMUP). All algorithms start with a network

where yi = 0 and xijk = 0 i,j ,k; the initial cost for

each link is cij = aijPA + PO (assuming for simplicity

that aijk = aij k). The main steps of each algorithm

are described below.

LCP: for each request, compute the shortest path P

using cij as static routing costs.

MUP: for each request, compute the shortest path up-

dating the routing costs of links used to route the cur-rent lightpath request. Using a pseudo-code notation,

for each lightpath sd

mailto:luca.chiaraviglio@polito.itmailto:luca.chiaraviglio@polito.itmailto:luca.chiaraviglio@polito.it

8/22/2019 dfrgrgccccccccccccccccccccccccccccccccccccccccccccccccccccccccccccccccccccccccccccccccccccccccccccccccccccccccccccc

http:///reader/full/dfrgrgccccccccccccccccccccccccccccccccccccccccccccccccccccccccccccccccccccccccccccccccccccccccccc 2/2

0

50

100

150

200

250

300

350

5 10 15 20 25 30

PTOT[kW]

N

LCP-FF

MUP-FF

OLMUP-FF

LB

Fig. 1: Power Consumption vs number of nodes randomphysical topology

compute the shortest path Psd using costs cij

cij = 0 (i, j) PsdOLMUP: at each iteration, select the lightpath to be

routed as the one that minimizes the incremental cost

(Lightpath Selection LS phase). Then route it us-

ing the MUPalgorithm (Routing Update RU phase).During LS, find the lightpath that has the minimum in-

cremental cost: for each lightpath sd not yet assigned

compute the shortest path Psd using costs cij

compute the incremental cost CP =

ijPsdcij

if CP < Cmin then Cmin = CP; s = s; d = d;

P = Psd; = sd

During RU, route on P using the MUPalgorithm.

Considering the fiber&wavelength assignment prob-

lem, we use in all cases a simple First-Fit strategy

(FF) which has been proved to be one of the most ef-

fective algorithms [1]: for each lightpath, considering

first powered-on fibers, wavelengths are sequentiallyscanned for availability on the whole path. If no wave-

length is found, a new fiber is powered on in each link.

In case no assignment is possible, a new path is com-

puted, forbidding links in the previously chosen path.

Finally, for all used fibers and OXCs, set xijk = 1 and

yi = 1 and compute Ptot as in Eq. 1.

To compare results, we define a rough lower bound

(LB) by considering that at least all OXCs which are

source or destination of a lightpath request must be

powered on, and that at least the cheapest fiber must

be used to exit from s or to arrive to d for each lightpath.

Performance Evaluation

Several scenarios were studied in [2]. We report here

results considering physical topologies which are either

bidirectional rings, or generic meshes (generated con-

sidering a probability 0.5 of having a link between any

two OXCs). We assume Kij = 10 and Fijk = 128,

and PA = PO = 1kW. The number of amplifiers on

each fiber aijk is instead a discrete random variable

uniformly distributed in [0, 10].

We first consider a set of randomly chosen light-

paths, so that there is a lightpath between any two

nodes with probability 0.5. Fig. 1 reports the total power

consumption required to route all lightpath requestsversus the number of OXCs N in the physical topology.

Results are obtained averaging over 10 independent

0

200

400

600

800

1000

1200

1400

1600

1800

5 10 15 20 25 30

PTOT[kW]

N

LCP-FF

MUP-FF

OLMUP-FF

LB

Fig. 2: Power Consumption vs number of nodes bidirec-tional ring physical topology

02468

10

500 550 600 650 700

Kon

ij

(i,j)ID

LCP-FFMUP-FF

OLMUP-FF

02468

10

0 10 20 30 40 50 60

Kon

ij

(i,j)IDFig. 3: Number of used fibers vs link ID random topology onthe left, and bidirectional ring on the right. N = 32.

runs. Using LCP-FF, which is almost power-unaware,

the power consumption of the network grows as 10N,

since no spatial reuse is enforced. Considering on the

contrary both the MUP-FF and OLMUP-FF heuristics,

much better results are obtained, due to the power-

aware routings, with the OLMUP-FF being very close

to the lower bound. The energy saving can be very sig-

nificant even for small networks, e.g., for N = 24 nodes

the power consumption is approximately reduced by a

factor of 5, i.e., around 200kW of saving.

Considering a bidirectional ring physical topology,Fig. 2 details PTOT versus N: also in this case

OLMUP-FF shows the best results. Notice that the total

power consumption is much larger in this scenario, and

the lower bound is not very tight. This is due to the reg-

ularity of the physical topology, in which path lengths

are larger [O(N) versus O(ln(N))], and to less alter-

natives in path selection. Still power saving achieved

by OLMUP-FF is larger than 400kW if N = 24.

Fig. 3 reports the number Konij of fibers powered on

for each link (omitting links where Kon = 0). It shows

that LCP-FF always uses more fibers (therefore more

power) than the other two heuristics which on the con-trary try to reuse as much as possible already used

links. This holds true for both physical topologies. In

case of the bidirectional physical topology, a larger per-

centage of links are required as expected.

While the considered scenario, with large numbers

of fibers on each link and of wavelengths per fiber com-

pared to the number of lightpaths, eases the reduction

of devices that must be powered on, our results still

bring evidence to the fact that new design criteria aimed

at power saving can be very effective.

References

1 H. Zang at al., A Review of RWA Approaches for WR Net-works, SPIE Optical Networks Mag, 2000

2 Y.Wu, Ms thesis; http://www.tlc.polito.it/wu.pdf.

http://www.tlc.polito.it/wu.pdfhttp://www.tlc.polito.it/wu.pdfhttp://www.tlc.polito.it/wu.pdf